Combinatorics of subgroups of Beidleman near-vector spaces

TL;DR

This paper explores the combinatorial structure of R-subgroups in finite-dimensional Beidleman near-vector spaces over nearfields, providing formulas and characterizations that reveal their generating sets and enumeration.

Contribution

It introduces a characterization of R-subgroups and derives formulas for their count and minimal generating sets, advancing understanding of near-vector space subgroup structure.

Findings

Smallest generating sets are significantly smaller than subgroup dimensions

Derived a formula for counting R-subgroups in n-dimensional near-vector spaces

Provided a characterization of R-subgroups in near-vector spaces

Abstract

Combinatorial aspects of R-subgroups of finite dimensional Beidleman near-vector spaces over nearfields are studied. A characterization of R-subgroups is used to obtain the smallest possible size of a generating set of a subgroup, which is much smaller than its dimension. Furthermore, a formula for the number of R-subgroups of an n-dimensional near-vector space is developed.